Numerical Renormalization Group Algorithms for Self-Similar Asymptotics of Partial Differential Equations
DOI10.1137/18M120004XzbMath1435.65183arXiv1707.05544OpenAlexW3004814610MaRDI QIDQ5222117
Long Lee, Gastão A. Braga, Frederico Furtado, Vincenzo Michael Isaia
Publication date: 31 March 2020
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1707.05544
critical exponentsasymptotic limitrenormalization group theoryself-similar dynamicsnumerical renormalization grouplogarithmic correctionsmarginal perturbations
Asymptotic behavior of solutions to PDEs (35B40) Critical exponents in context of PDEs (35B33) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Self-similar solutions to PDEs (35C06)
Cites Work
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- Renormalization group calculation of asymptotically self-similar dynamics
- A boundary value problem for the KdV equation: comparison of finite-difference and Chebyshev methods
- Asymptotic behaviour of nonlinear parabolic equations with critical exponents. A dynamical systems approach
- On the asymptotic behavior of solutions to nonlinear, dispersive, dissipative wave equations
- Universal self-similarity of porous media equation with absorption: the critical exponent case.
- Decay of solutions to nonlinear parabolic equations: renormalization and rigorous results
- Renormalization study of two-dimensional convergent solutions of the porous medium equation
- Regularity of interfaces in diffusion processes under the influence of strong absorption
- Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities
- A renormalization group approach to blow-up and extinction exponents.
- Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld
- Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity
- An iterative grid redistribution method for singular problems in multiple dimensions
- Interactions and asymptotics of dispersive shock waves -- Korteweg-de Vries equation
- Numerical simulation of universal finite time behavior for parabolic IVP via geometric renormalization group
- Renormalization methods for higher order differential equations
- Nonlinear dynamics and breakup of free-surface flows
- RENORMALIZATION AND ASYMPTOTICS
- Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior
- Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
- Stability of self-similar solutions for van der Waals driven thin film rupture
- The One-Dimensional Nonlinear Heat Equation with Absorption: Regularity of Solutions and Interfaces
- A rescaling algorithm for the numerical calculation of blowing-up solutions
- Renormalization and scaling methods for nonlinear parabolic systems
- Renormalization group and asymptotics of solutions of nonlinear parabolic equations
- A Nonhomogeneous Boundary-Value Problem for the Korteweg–de Vries Equation Posed on a Finite Domain
- The global dynamics of isothermal chemical systems with critical nonlinearity
- Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients
- On Some Reaction-Diffusion Systems with Nonlinear Diffusion Arising in Biology
- A Renormalization Method for Modulational Stability of Quasi-Steady Patterns in Dispersive Systems
- On self-similar solutions of Barenblatt's nonlinear filtration equation
- Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$
- Quantum Electrodynamics at Small Distances
- Focusing of an elongated hole in porous medium flow
